If one-fourth of one-third of one-half of a number equals 15, what is the original number?

Introduction / Context:
This problem is a straightforward application of multiplying fractions to represent successive parts of a number. It assesses your ability to translate nested fractional statements into a single fraction and then invert that operation to recover the original number.

Given Data / Assumptions:

• Let the number be N.
• (1/4) * (1/3) * (1/2) * N = 15.
• All quantities are real; N is positive by context.

Concept / Approach:
Multiply the fractions to get a single factor applied to N. Then solve for N by dividing 15 by that factor (equivalently multiplying by its reciprocal). Order does not matter because multiplication is associative and commutative.

Step-by-Step Solution:

Verification / Alternative check:
Compute backward: half of 360 is 180; one-third of 180 is 60; one-fourth of 60 is 15. The chain matches the given statement exactly.

Why Other Options Are Wrong:
72, 120, 180, and 240 each produce a final value different from 15 when the same fractional steps are applied.

Common Pitfalls:
Adding the fractions instead of multiplying, or taking the sequence in reverse without checking each stage.

Final Answer:
360